The charge transfer compound CuTCNQ (TCNQ = 7,7,8,8-Tetracyanoquinodimethane) exhibits switching between two electrical resistance states when subject to an electric field. It is known that the the material has two structural phases (I and II) each with very different electrical conductivities and magnetic properties. While the electrical properties of CuTCNQ has been investigated by many, the magnetic properties have attracted very little interest even though phase II is ferromagnetic below 10K while phase I is essentially diamagnetic. We propose to use muon spin rotation/relaxation to investigate the magnetic properties of both phases of CuTCNQ. The ferromagnetic transition in CuTCNQ-II will be studied in zero field and in longitudinal fields. CuTCNQ-I will be investigated in zero field to look for evidence of antiferromagnetically coupled radical spins bound to the TCNQ anions.